\chapter{Observation Processing Pipeline}
\label{ch:observation_pipeline}

\section{Overview of Observation Ingestion Architecture}

The GSI observation processing pipeline implements a sophisticated two-stage approach designed to efficiently handle the diverse range of meteorological observations while maintaining parallel scalability across distributed computing environments. This architecture separates observation reading from distribution, enabling optimal processor utilization and memory management for large-scale operational data assimilation systems.

\section{Two-Stage Processing Framework}
\label{sec:two_stage_framework}

The GSI observation pipeline employs a carefully designed two-stage processing approach that maximizes computational efficiency and parallel scalability:

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[node distance=2cm]
\node (input) [rectangle, draw, text width=3cm, text centered] {Native Observation Files\\(BUFR, NetCDF, GRIB)};
\node (stage1) [rectangle, draw, below of=input, text width=4cm, text centered] {Stage 1: Parallel Reading\\Master-Worker Pattern};
\node (intermediate) [rectangle, draw, below of=stage1, text width=3cm, text centered] {Intermediate Files\\obs\_input.*};
\node (stage2) [rectangle, draw, below of=intermediate, text width=4cm, text centered] {Stage 2: Observation Scattering\\Geographic Distribution};
\node (local) [rectangle, draw, below of=stage2, text width=3cm, text centered] {Local Processor Files\\pe*.obs-type\_outer-loop};

\draw [arrow] (input) -- (stage1);
\draw [arrow] (stage1) -- (intermediate);
\draw [arrow] (intermediate) -- (stage2);
\draw [arrow] (stage2) -- (local);
\end{tikzpicture}
\caption{GSI Two-Stage Observation Processing Pipeline}
\label{fig:obs_pipeline}
\end{figure}

\section{Stage 1: Parallel Reading into Intermediate Files}
\label{sec:stage1_reading}

\subsection{Master-Worker Coordination}

The first stage implements a master-worker parallel pattern where observation type-specific readers operate on dedicated processor subsets. This approach provides several advantages:

\begin{itemize}
\item \textbf{Concurrent Processing}: Multiple observation types processed simultaneously on different processor groups
\item \textbf{I/O Optimization}: Specialized readers optimized for specific data formats and access patterns  
\item \textbf{Memory Efficiency}: Only active observation types consume memory resources on designated processors
\item \textbf{Error Isolation}: Processing failures isolated to specific observation types without system-wide impact
\end{itemize}

The master routine coordinates reader activation based on observation type configuration:

\begin{lstlisting}[language=Fortran,caption=Observation Type Coordination]
do obstype = 1, num_obstypes
    if (process_obstype(obstype) .and. mype_obstype(obstype)) then
        select case (obstype)
            case ('prepbufr')
                call read_prepbufr(mype, nread, ndata, infile, obstype)
            case ('satwnd')
                call read_satwnd(mype, nread, ndata, infile, obstype)
            case ('bufrtovs')
                call read_bufrtovs(mype, nread, ndata, infile, obstype)
            ! Additional observation types...
        end select
    endif
end do
\end{lstlisting}

\subsection{Intermediate File Format}

The intermediate \texttt{obs\_input.*} files employ a standardized binary format optimized for subsequent processing:

\begin{equation}
\text{Record Structure} = \{n_{obs}, n_{param}, [\text{obs}_i]_{i=1}^{n_{obs}}\}
\end{equation}

Where each observation record contains:
\begin{itemize}
\item Location coordinates (latitude, longitude, pressure/height)
\item Observation value and estimated error variance
\item Quality control flags and metadata
\item Time information relative to analysis window
\item Observation type and subtype identifiers
\end{itemize}

\section{Reader Subroutines}
\label{sec:pipeline_reader_subroutines}

\subsection{Conventional Data Reader: read\_prepbufr}

The \texttt{read\_prepbufr} subroutine processes conventional meteorological observations from PrepBUFR files, which contain quality-controlled surface, upper-air, and aircraft observations:

\subsubsection{Data Types Processed}

\begin{table}[htbp]
\centering
\caption{PrepBUFR Observation Types}
\label{tab:prepbufr_types}
\begin{tabular}{|l|l|p{8cm}|}
\hline
\textbf{Type} & \textbf{Code} & \textbf{Description} \\
\hline
Temperature & \texttt{t} & Surface, radiosonde, aircraft temperature observations \\
\hline
Wind & \texttt{uv} & Surface, rawinsonde, pilot balloon wind vectors \\
\hline
Specific Humidity & \texttt{q} & Moisture observations from radiosondes and aircraft \\
\hline
Surface Pressure & \texttt{ps} & Station pressure observations with terrain corrections \\
\hline
Precipitable Water & \texttt{pw} & GPS-derived total column water vapor \\
\hline
Wind Speed & \texttt{spd} & Scalar wind speed from surface stations and buoys \\
\hline
Cloud Parameters & \texttt{cld} & Cloud fraction and height information \\
\hline
Visibility & \texttt{vis} & Surface visibility observations \\
\hline
Gust & \texttt{gust} & Peak wind gust measurements \\
\hline
\end{tabular}
\end{table}

\subsubsection{Quality Control Integration}

The PrepBUFR reader implements comprehensive quality control:

\begin{equation}
\text{QC\_flag} = \begin{cases}
0 & \text{if } |\text{obs} - \text{background}| \leq k \sigma_{qc} \\
1 & \text{if } k \sigma_{qc} < |\text{obs} - \text{background}| \leq 2k \sigma_{qc} \\
2 & \text{if } |\text{obs} - \text{background}| > 2k \sigma_{qc}
\end{cases}
\end{equation}

Where $k$ is a quality control factor (typically 3-5) and $\sigma_{qc}$ combines observation and background error estimates.

\subsection{Satellite Wind Reader: read\_satwnd}

The \texttt{read\_satwnd} subroutine processes atmospheric motion vectors (AMVs) derived from satellite imagery:

\begin{itemize}
\item \textbf{Derivation Methods}: Feature tracking, water vapor tracking, and cloud motion vectors
\item \textbf{Quality Indicators}: Expected error estimates and quality index values
\item \textbf{Height Assignment}: Pressure level assignment based on brightness temperature or CO2 slicing
\item \textbf{Thinning Procedures}: Spatial and temporal thinning to reduce observation correlation
\end{itemize}

The height assignment uncertainty is parameterized as:

\begin{equation}
\sigma_p^2 = \sigma_{base}^2 + (\alpha \Delta p)^2
\end{equation}

Where $\sigma_{base}$ is the base pressure error, $\Delta p$ is the pressure difference from the nearest standard level, and $\alpha$ is a scaling factor.

\subsection{Radiance Readers}
\label{sec:radiance_readers}

\subsubsection{TOVS Reader: read\_bufrtovs}

The \texttt{read\_bufrtovs} subroutine processes Television Infrared Observation Satellite (TOVS) radiance data:

\begin{itemize}
\item \textbf{AMSUA}: Advanced Microwave Sounding Unit-A for temperature profiling
\item \textbf{AMSUB/MHS}: Microwave humidity sounders
\item \textbf{HIRS}: High Resolution Infrared Radiation Sounder
\item \textbf{MSU}: Microwave Sounding Unit
\item \textbf{SSU}: Stratospheric Sounding Unit
\end{itemize}

The radiance observation equation follows:

\begin{equation}
I_{\nu,obs} = I_{\nu,calc}(T, q, O_3, ...) + \epsilon_{\nu}
\end{equation}

Where $I_{\nu,obs}$ is the observed radiance at frequency $\nu$, $I_{\nu,calc}$ is the calculated radiance from the radiative transfer model, and $\epsilon_{\nu}$ represents observation error.

\subsubsection{Advanced IR Sounder: read\_airs}

The \texttt{read\_airs} routine processes Atmospheric Infrared Sounder (AIRS) hyperspectral radiance observations:

\begin{itemize}
\item \textbf{Spectral Coverage}: 2378 infrared channels spanning 3.7-15.4 μm
\item \textbf{Channel Selection}: Intelligent channel subset selection based on atmospheric conditions
\item \textbf{Cloud Detection}: Multi-channel cloud screening algorithms
\item \textbf{Bias Correction}: Angle-dependent and scene-dependent bias removal
\end{itemize}

\subsubsection{Next-Generation Sounders}

Modern sounder readers handle advanced instruments:

\begin{itemize}
\item \textbf{ATMS (read\_atms)}: Advanced Technology Microwave Sounder with enhanced spatial resolution
\item \textbf{CrIS (read\_cris)}: Cross-track Infrared Sounder providing hyperspectral infrared observations
\item \textbf{IASI (read\_iasi)}: Infrared Atmospheric Sounding Interferometer with high spectral resolution
\end{itemize}

\subsection{Imager Radiance Readers}

\subsubsection{GOES Instruments}

\begin{itemize}
\item \textbf{GOES Sounder (read\_goesndr)}: Multi-channel infrared and visible sounder observations
\item \textbf{GOES Imager (read\_goesimg)}: High temporal resolution imaging observations for nowcasting applications
\end{itemize}

\subsubsection{International Imagers}

\begin{itemize}
\item \textbf{SEVIRI (read\_seviri)}: Spinning Enhanced Visible and Infrared Imager from Meteosat Second Generation
\item \textbf{AVHRR (read\_avhrr)}: Advanced Very High Resolution Radiometer from NOAA polar orbiters
\end{itemize}

\subsection{Microwave Imager Readers}

\subsubsection{Passive Microwave Instruments}

\begin{itemize}
\item \textbf{SSM/I (read\_ssmi)}: Special Sensor Microwave/Imager for ocean surface parameters
\item \textbf{AMSR-E (read\_amsre)}: Advanced Microwave Scanning Radiometer-Earth Observing System
\item \textbf{SSMIS (read\_ssmis)}: Special Sensor Microwave Imager/Sounder combining imaging and sounding capabilities
\end{itemize}

These readers process brightness temperature observations for:
\begin{equation}
T_B(\nu) = \int_0^{\infty} B(T, \nu) W(\nu, \tau) d\tau
\end{equation}

Where $T_B$ is brightness temperature, $B(T, \nu)$ is the Planck function, and $W(\nu, \tau)$ is the weighting function.

\subsection{Specialized Observation Readers}

\subsubsection{GPS Radio Occultation: read\_gps}

The \texttt{read\_gps} subroutine processes GPS radio occultation observations providing atmospheric refractivity and bending angle profiles:

\begin{equation}
N = 77.6 \frac{P}{T} + 3.73 \times 10^5 \frac{e}{T^2}
\end{equation}

Where $N$ is refractivity, $P$ is pressure, $T$ is temperature, and $e$ is water vapor pressure.

\subsubsection{Radar Observations}

\begin{itemize}
\item \textbf{Doppler Radar Winds (read\_radar)}: Radial velocity measurements from weather radar networks
\item \textbf{Radar Reflectivity (read\_RadarRef\_mosaic)}: Precipitation intensity and hydrometeor information
\end{itemize}

The radar observation equation relates radial velocity to three-dimensional wind:

\begin{equation}
V_r = \mathbf{u} \cdot \hat{\mathbf{r}} = u \sin(\phi) \cos(\theta) + v \cos(\phi) \cos(\theta) + w \sin(\theta)
\end{equation}

Where $V_r$ is radial velocity, $\mathbf{u} = (u, v, w)$ is the wind vector, and $(\phi, \theta)$ define the radar beam direction.

\subsubsection{Lidar Wind Observations: read\_lidar}

Doppler lidar wind observations provide high-resolution wind profiles:

\begin{itemize}
\item \textbf{Aerosol Backscatter}: Vertical aerosol distribution information
\item \textbf{Wind Speed and Direction}: Three-dimensional wind vector retrieval
\item \textbf{Atmospheric Boundary Layer}: High-resolution boundary layer structure
\end{itemize}

\subsection{Chemical and Trace Gas Observations}

\subsubsection{Ozone Observations: read\_ozone}

Multiple ozone observation sources are processed:

\begin{itemize}
\item \textbf{SBUV}: Solar Backscatter Ultraviolet total column and profile ozone
\item \textbf{OMI}: Ozone Monitoring Instrument total column measurements
\item \textbf{MLS}: Microwave Limb Sounder stratospheric ozone profiles
\item \textbf{GOME/SCIAMACHY}: European ozone monitoring instruments
\end{itemize}

\subsubsection{Aerosol Observations: read\_NASA\_LaRC}

NASA Langley Research Center aerosol observations include:

\begin{itemize}
\item \textbf{MODIS Aerosol Optical Depth}: Satellite-derived aerosol loading
\item \textbf{AERONET**: Ground-based aerosol optical properties
\item \textbf{CALIPSO**: Vertical aerosol profiles from space-based lidar
\end{itemize}

\subsubsection{Air Quality Observations}

\begin{itemize}
\item \textbf{PM2.5 (read\_anowbufr)}: Particulate matter concentration measurements
\item \textbf{Lightning (read\_lightning)**: Lightning flash rate and location data for convective initiation
\item \textbf{PBL Height (read\_pblh)**: Planetary boundary layer depth observations
\end{itemize}

\section{Stage 2: Observation Scattering}
\label{sec:stage2_scattering}

\subsection{Geographic Distribution Framework: obs\_para}

The \texttt{obs\_para} subroutine implements the second stage of observation processing, distributing observations to analysis processors based on geographic location:

\subsubsection{Spatial Domain Decomposition}

Each analysis processor is assigned a geographic subdomain:

\begin{equation}
\Omega_p = \{(x,y) : x_{min,p} \leq x \leq x_{max,p}, y_{min,p} \leq y \leq y_{max,p}\}
\end{equation}

Where $\Omega_p$ represents the subdomain assigned to processor $p$, with appropriate boundary overlaps for interpolation operations.

\subsubsection{Observation Selection Criteria}

Observations are assigned to processors based on multiple criteria:

\begin{itemize}
\item \textbf{Geographic Location}: Primary assignment based on observation coordinates
\item \textbf{Influence Radius}: Inclusion of observations within specified influence radius of subdomain
\item \textbf{Observation Type**: Type-specific influence radius and processing requirements
\item \textbf{Load Balancing**: Dynamic adjustment to maintain computational balance
\end{itemize}

The observation influence criterion follows:

\begin{equation}
\text{Include obs}_i \text{ if } \min_{(x,y) \in \Omega_p} \sqrt{(x_i - x)^2 + (y_i - y)^2} \leq R_{influence}
\end{equation}

\subsection{Processor-Local File Generation}

Each processor creates local observation files with standardized naming convention:

\begin{lstlisting}[language=Fortran,caption=Local Observation File Naming]
filename = 'pe' // trim(adjustl(processor_id)) // '.' // &
           trim(obstype) // '_' // trim(adjustl(outer_loop_id))
\end{lstlisting}

\subsubsection{File Format Optimization}

The processor-local files employ binary format optimized for analysis operations:

\begin{itemize}
\item \textbf{Sequential Access}: Optimized for observation loop processing during analysis
\item \textbf{Compact Storage**: Minimal memory footprint while preserving essential information
\item \textbf{Platform Independence**: Portable binary format across different computing architectures
\item \textbf{Error Recovery**: Built-in consistency checking and error recovery mechanisms
\end{itemize}

\section{Observation Preprocessing and Quality Control}
\label{sec:obs_preprocessing}

\subsection{Temporal Window Processing}

Observations undergo temporal processing to align with analysis requirements:

\begin{equation}
w_t = \begin{cases}
1 - \frac{|t_{obs} - t_{analysis}|}{t_{window}} & \text{if } |t_{obs} - t_{analysis}| \leq t_{window} \\
0 & \text{otherwise}
\end{cases}
\end{equation}

Where $w_t$ is the temporal weight, $t_{obs}$ is observation time, $t_{analysis}$ is analysis time, and $t_{window}$ is the assimilation window half-width.

\subsection{Spatial Thinning Procedures}

High-density observation types undergo spatial thinning:

\begin{itemize}
\item \textbf{Regular Grid Thinning}: Systematic selection on uniform spatial grids
\item \textbf{Distance-Based Thinning**: Minimum separation distance enforcement
\item \textbf{Quality-Based Thinning**: Retention of highest quality observations within each spatial cell
\item \textbf{Adaptive Thinning**: Dynamic thinning based on local observation density
\end{itemize}

\subsection{Bias Correction Application}

Systematic bias correction is applied to appropriate observation types:

\begin{equation}
y_{corrected} = y_{original} - \sum_i \beta_i \text{predictor}_i
\end{equation}

Where $\beta_i$ are bias correction coefficients and predictors include:
\begin{itemize}
\item Scan angle and airmass-dependent terms for satellite radiances  
\item Temperature-dependent bias for aircraft observations
\item Seasonal and diurnal cycle corrections
\item Model-dependent systematic errors
\end{itemize}

\section{Performance Optimization and Scalability}
\label{sec:obs_performance}

\subsection{I/O Optimization Strategies}

\begin{itemize}
\item \textbf{Asynchronous Reading**: Overlapping I/O operations with computational tasks
\item \textbf{Buffer Management**: Optimized buffer sizes for different observation file types
\item \textbf{Parallel I/O**: Coordinated reading using MPI-IO for large observation files
\item \textbf{Compression Support**: Transparent handling of compressed observation files
\end{itemize}

\subsection{Memory Management}

Efficient memory utilization includes:

\begin{itemize}
\item \textbf{Dynamic Allocation**: Memory allocation based on actual observation counts
\item \textbf{Memory Pooling**: Reuse of memory buffers across observation types
\item \textbf{Streaming Processing**: Processing observations in chunks to minimize memory requirements
\item \textbf{Garbage Collection**: Systematic cleanup of temporary data structures
\end{itemize}

\subsection{Load Balancing}

The observation pipeline implements sophisticated load balancing:

\begin{equation}
\text{Load}_p = \sum_i N_{obs,i,p} \times C_{computational,i}
\end{equation}

Where $N_{obs,i,p}$ is the number of observations of type $i$ assigned to processor $p$, and $C_{computational,i}$ represents the computational cost per observation for type $i$.

The sophisticated observation processing pipeline ensures efficient ingestion, quality control, and distribution of diverse meteorological observations, providing the foundation for accurate and timely data assimilation within the GSI analysis framework.